Blender on Linux - list of AMD GPUs that work with Cycles/OpenCL
This is a list of AMD GPUs known running together with OpenCL and Blender Cycles. It is composed by either personal experience or from sources on the web:

╔═════════════════════╦═════════╦════════════╦════════════╦════════════╦════════╗
║         GPU         ║   OS    ║ OS version ║ Blender v. ║   Driver   ║ Source ║
╠═════════════════════╬═════════╬════════════╬════════════╬════════════╬════════╣
║    Radeon cards     ║         ║            ║            ║            ║        ║
║ RX580               ║ Xubuntu ║ 18.04.02   ║ 2.8beta    ║ OpenCL-Pro ║      5 ║
║ RX580               ║ Linux*  ║ N/A        ║ 2.79       ║ N/A        ║    1,3 ║
║ RX470 4GB           ║ Kubuntu ║ 16.04      ║ 2.78       ║ AMDGPU-Pro ║      2 ║
║ RX Vega 64          ║ Arch,   ║ N/A        ║ 2.79       ║ AMDGPU &amp;   ║      4 ║
║                     ║ custom kernel, libdrm downgrade   ║ AMD OpenCL ║        ║
║ RX480               ║ Linux*  ║ N/A        ║ 2.79_build ║ N/A        ║      3 ║
║ RX Vega 56          ║ Linux*  ║ N/A        ║ 2.79_build ║ N/A        ║      3 ║
║ RX Vega 64          ║ Linux*  ║ N/A        ║ 2.79_build ║ N/A        ║      3 ║
║ RX Vega Frontier E. ║ Linux*  ║ N/A        ║ 2.79_build ║ N/A        ║      3 ║
║ Pro WX 7100         ║ Linux*  ║ N/A        ║ 2.79_build ║ N/A        ║      3 ║
║ Pro WX 7100 DUO     ║ Linux*  ║ N/A        ║ 2.79_build ║ N/A        ║      3 ║
╚═════════════════════╩═════════╩════════════╩════════════╩════════════╩════════╝



* likely Ubuntu or a derivate (officially supported), see this comment. Also means that AMDs OpenCL implementation must've been used, as there's no other known working so far

sources:
1, 
2,
3
4: user gandalf3
   5: myself, using Xubuntu 18.04.02 with an all open stack (standard) plus the OpenCL portion from the closed AMDGPU-Pro driver


This list is obviously far from complete, it's just meant as a start. I'll gather more and more information in the near future.

Feel free to edit, improve and add to this list to complete it and make it comprehensive in the end!

P.S.: The table was made with https://senseful.github.io/text-table/, as the standard SE markdown does not support tables in any way, see here.